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Q. If a 6Ω and a 3Ω resistor are connected in parallel, what is the equivalent resistance? (2022)

A. 2Ω
B. 4Ω
C. 1.5Ω
D. 9Ω

Solution

Using the formula for parallel resistors: 1/R_eq = 1/R1 + 1/R2 = 1/6 + 1/3 = 1/6 + 2/6 = 3/6. Therefore, R_eq = 2Ω.

Correct Answer: A — 2Ω

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Q. If a 6Ω resistor is connected in parallel with a 3Ω resistor, what is the equivalent resistance? (2023)

A. 2Ω
B. 1.5Ω
C. 4Ω
D. 9Ω

Solution

Using the formula 1/R_eq = 1/R1 + 1/R2, we get 1/R_eq = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, thus R_eq = 2Ω.

Correct Answer: A — 2Ω

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Q. If a 9V battery is connected to a 3Ω resistor, what is the current flowing through it? (2021)

A. 1A
B. 2A
C. 3A
D. 4A

Solution

Using Ohm's law, I = V/R = 9V / 3Ω = 3A.

Correct Answer: B — 2A

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Q. If a 9V battery is connected to a 3Ω resistor, what is the energy consumed in 10 seconds? (2023)

A. 30J
B. 90J
C. 60J
D. 45J

Solution

Power (P) = V²/R = 9²/3 = 27W. Energy (E) = P * t = 27W * 10s = 270J.

Correct Answer: B — 90J

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Q. If a 9V battery is connected to a 3Ω resistor, what is the power dissipated in the resistor? (2023)

A. 3W
B. 9W
C. 6W
D. 12W

Solution

Power (P) can be calculated using P = V²/R = (9V)² / 3Ω = 81 / 3 = 27W.

Correct Answer: A — 3W

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Q. If a 9V battery is connected to a 3Ω resistor, what is the voltage drop across the resistor? (2023)

A. 3V
B. 6V
C. 9V
D. 12V

Solution

The voltage drop across the resistor is equal to the battery voltage, which is 9V.

Correct Answer: C — 9V

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Q. If a = 2 and b = 3, what is the value of a^3 + b^3? (2021)

A. 35
B. 27
C. 10
D. 8

Solution

a^3 = 2^3 = 8 and b^3 = 3^3 = 27, so 8 + 27 = 35.

Correct Answer: A — 35

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Q. If A = 2i + 3j and B = 3i + 4j, what is the angle between A and B? (2021)

A. 0 degrees
B. 45 degrees
C. 90 degrees
D. 180 degrees

Solution

cos(θ) = (A · B) / (|A||B|) = (2*3 + 3*4) / (√(2^2 + 3^2) * √(3^2 + 4^2)) = 0.7071, θ = 45 degrees.

Correct Answer: B — 45 degrees

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Q. If a = 3 and b = 4, what is a^2 + b^2? (2017)

A. 25
B. 20
C. 15
D. 10

Solution

a^2 = 9 and b^2 = 16, so 9 + 16 = 25.

Correct Answer: A — 25

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Q. If a = 3 and b = 4, what is the value of a^2 + b^2? (2019)

A. 25
B. 12
C. 7
D. 16

Solution

a^2 = 9 and b^2 = 16, so 9 + 16 = 25.

Correct Answer: A — 25

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Q. If A = 3i + 4j and B = 2i - j, what is A + B? (2021)

A. 5i + 3j
B. 5i + 5j
C. 1i + 5j
D. 1i + 3j

Solution

A + B = (3i + 4j) + (2i - j) = (3 + 2)i + (4 - 1)j = 5i + 3j.

Correct Answer: A — 5i + 3j

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Q. If a = 4 and b = 2, what is the value of a^2 + b^2? (2020)

A. 20
B. 16
C. 18
D. 14

Solution

a^2 = 16 and b^2 = 4, so 16 + 4 = 20.

Correct Answer: A — 20

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Q. If A = 4i + 2j and B = -i + 3j, what is the scalar triple product A · (B × A)? (2023)

A. 0
B. 8
C. 12
D. 16

Solution

B × A = |i  j  k| |-1  3  0| |4  2  0| = 0, hence A · (B × A) = 0.

Correct Answer: A — 0

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Q. If A = 5i + 12j, what is the unit vector in the direction of A? (2021)

A. (5/13)i + (12/13)j
B. (12/13)i + (5/13)j
C. (5/12)i + (12/5)j
D. (12/5)i + (5/12)j

Solution

Unit vector = A / |A| = (5i + 12j) / √(5^2 + 12^2) = (5/13)i + (12/13)j.

Correct Answer: A — (5/13)i + (12/13)j

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Q. If A = i + 2j + 3k and B = 4i + 5j + 6k, what is A - B? (2023)

A. -3i - 3j - 3k
B. -3i - 3j + 3k
C. 3i + 3j + 3k
D. 3i + 3j - 3k

Solution

A - B = (1 - 4)i + (2 - 5)j + (3 - 6)k = -3i - 3j - 3k.

Correct Answer: A — -3i - 3j - 3k

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Q. If A = {2, 4, 6} and B = {1, 2, 3}, what is A ∩ B?

A. {2}
B. {4, 6}
C. {1, 2, 3}
D. {}

Solution

The intersection A ∩ B includes elements that are in both A and B. Here, A ∩ B = {2}.

Correct Answer: A — {2}

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Q. If A = {x | x is a prime number less than 10}, what is A?

A. {2, 3, 5, 7}
B. {1, 2, 3, 4}
C. {2, 4, 6, 8}
D. {3, 5, 7, 9}

Solution

The prime numbers less than 10 are 2, 3, 5, and 7. Therefore, A = {2, 3, 5, 7}.

Correct Answer: A — {2, 3, 5, 7}

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Q. If A = {x | x is an even number} and B = {x | x is a multiple of 3}, what is A ∪ B?

A. {0, 2, 4, 6, ...}
B. {0, 3, 6, 9, ...}
C. {0, 2, 3, 4, 6, 9, ...}
D. {0, 1, 2, 3, ...}

Solution

The union A ∪ B includes all even numbers and all multiples of 3. Thus, A ∪ B = {0, 2, 3, 4, 6, 9, ...}.

Correct Answer: C — {0, 2, 3, 4, 6, 9, ...}

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Q. If a bag contains 4 green and 6 yellow marbles, what is the probability of picking a green marble?

A. 2/5
B. 4/10
C. 4/6
D. 1/3

Solution

Total marbles = 4 + 6 = 10. Probability of green marble = 4/10 = 2/5.

Correct Answer: A — 2/5

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Q. If a bag contains 4 green and 6 yellow marbles, what is the probability of picking a yellow marble?

A. 2/5
B. 3/5
C. 4/5
D. 1/5

Solution

Total marbles = 4 + 6 = 10. Probability of yellow = 6/10 = 3/5.

Correct Answer: B — 3/5

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Q. If a body is moving in a circular path with a constant speed, what is its acceleration? (2023)

A. Zero
B. Tangential
C. Centripetal
D. Radial

Solution

The body experiences centripetal acceleration directed towards the center of the circular path.

Correct Answer: C — Centripetal

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Q. If a body is moving in a circular path with a constant speed, what type of acceleration does it experience?

A. Centripetal acceleration
B. Linear acceleration
C. Angular acceleration
D. No acceleration

Solution

A body moving in a circular path experiences centripetal acceleration directed towards the center of the circle.

Correct Answer: A — Centripetal acceleration

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Q. If a capacitor is charged to 12V and has a capacitance of 6μF, what is the stored energy? (2022)

A. 0.432 mJ
B. 0.072 mJ
C. 0.864 mJ
D. 0.216 mJ

Solution

Energy = 0.5 × C × V² = 0.5 × 6 × 10^-6 × 12² = 0.432 mJ.

Correct Answer: A — 0.432 mJ

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Q. If a capacitor is charged to a voltage of 10V and has a capacitance of 5μF, what is the charge on the capacitor? (2022)

A. 50μC
B. 100μC
C. 10μC
D. 5μC

Solution

Using the formula Q = CV, the charge Q = 5μF * 10V = 50μC.

Correct Answer: A — 50μC

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Q. If a capacitor is charged to a voltage of 5 V and then disconnected from the battery, what happens to the charge on the capacitor if the voltage is increased to 10 V? (2023)

A. Charge increases
B. Charge decreases
C. Charge remains the same
D. Charge becomes zero

Solution

When the voltage is increased to 10 V, the charge on the capacitor increases because charge (Q) is directly proportional to voltage (V) for a given capacitance.

Correct Answer: A — Charge increases

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Q. If a car accelerates from rest to a speed of 20 m/s, and its mass is 1000 kg, what is the kinetic energy gained by the car? (2021)

A. 200,000 J
B. 100,000 J
C. 50,000 J
D. 400,000 J

Solution

Kinetic Energy (KE) = 0.5 × mass (m) × velocity² (v²). KE = 0.5 × 1000 kg × (20 m/s)² = 200,000 J.

Correct Answer: B — 100,000 J

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Q. If a car accelerates from rest to a speed of 20 m/s, and its mass is 1000 kg, what is the kinetic energy of the car at that speed? (2020)

A. 200 J
B. 1000 J
C. 2000 J
D. 4000 J

Solution

Kinetic Energy = 0.5 × mass × velocity² = 0.5 × 1000 kg × (20 m/s)² = 200000 J = 2000 J

Correct Answer: C — 2000 J

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Q. If a car accelerates from rest to a speed of 20 m/s, what is the kinetic energy of the car if its mass is 1000 kg?

A. 200,000 J
B. 100,000 J
C. 50,000 J
D. 400,000 J

Solution

Kinetic Energy = 0.5 × mass × velocity² = 0.5 × 1000 kg × (20 m/s)² = 200,000 J

Correct Answer: B — 100,000 J

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Q. If a car travels at a speed of 60 km/h, how far will it travel in 2 hours? (2022)

A. 120 km
B. 100 km
C. 150 km
D. 90 km

Solution

Distance = Speed × Time = 60 km/h × 2 h = 120 km.

Correct Answer: A — 120 km

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Q. If a car with a mass of 1200 kg is moving at a speed of 15 m/s, what is its kinetic energy? (2021)

A. 13500 J
B. 9000 J
C. 18000 J
D. 27000 J

Solution

Kinetic Energy = 0.5 × mass × velocity² = 0.5 × 1200 kg × (15 m/s)² = 13500 J

Correct Answer: A — 13500 J

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